%0 Journal Article %A Mazzocco, Marta %D 2015 %T Non-symmetric basic hypergeometric polynomials and representation theory for confluent Cherednik algebras %U https://repository.lboro.ac.uk/articles/journal_contribution/Non-symmetric_basic_hypergeometric_polynomials_and_representation_theory_for_confluent_Cherednik_algebras/9385559 %2 https://repository.lboro.ac.uk/ndownloader/files/16998758 %K DAHA %K Cherednik algebra %K q-Askey scheme %K Askey-Wilson polynomials %K Mathematical Sciences not elsewhere classified %X In this paper we introduce a basic representation for the confluent Cherednik algebras HV, HIII, HD7 III and HD8 III defined in arXiv:1307.6140. To prove faithfulness of this basic representation, we introduce the non-symmetric versions of the continuous dual q- Hahn, Al-Salam{Chihara, continuous big q-Hermite and continuous q-Hermite polynomials. %I Loughborough University